1.

Solve for x : `5+13+21+......+x=2139`

Answer» Here, `a=5, d=13-5=8`
Let `T_(n)=x`
`:. S_(n)=2139`
`:. (n)/(2) [2xx5+(n-1)8]=2139`
`rArr n(5+4n-4)=2139 rArr 4n^(2)+n-2139=0`
`rArr 4n^(2)-92n+93n-2139=0 rArr (n-23)(4n+93)=0`
`:. n=23 or n=-(93)/(4)`
since `n gt 0`, we have n=23
`:. x = T_(n)=a+(n-1)d=5+(23-1)(8)`
`rArr x=181`


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